I am about to enter an Engineering program after several years out of school. I took high-school calculus ten years ago but I was not a good student and mainly coasted through the work. I had decent marks (80+) but no retention of the theory.

The university has provided me with a 50-page booklet to help brush up on my math skills but I am having some difficulty as I am almost starting from scratch. This site has been a huge help so far but there is one problem I can't figure out and cannot find anything analogous to it in the guides.

I need to simplify the following equation:

( ( y / x ) + x) / ( 2 / x )

The solution at the back of the book is: ( y - x^2 )/2

My workflow is as follows:

1. ( ( y / x ) + x) / ( 2 / x )

2. Multiply by x^-1 (or 1/x):

<( ( y / x ) + x) / ( 2 / x )> * (x^-1)

3. Which results in:

(y + x(x^-1)) / 2

And this is where I am stuck. Every attempt I make to get past this just turns the whole thing into a disorganized mess and it is clear I am overlooking something important. I don't understand how to treat the x(x^-1) nor do I understand how the solution converts "y + x" to "y - x". I've been able to work backwards from the solution for the other questions I did incorrectly and figure out where I went wrong, but I am having no luck here.

I don't even understand what kind of equation this is so I have been unable to find any examples. I hope this is in the right place and I hope somebody can help me out!

I have tried the steps indicated on the site, and am getting closer to the answer. But I still cannot figure out where the minus sign is coming from! There are no negatives whatsoever in the expression so I don't understand how this is happening.

Haha, that certainly explains that! I was tearing my hair out trying to figure out what the heck was wrong. I've even had my roommate come verify the question and answer (without telling them what I thought it was) to make sure I hadn't misread it or something.